This paper presents a comprehensive review of the method of liquid phase epitaxy (LPE) of semiconductors. In Sect. 1 the physical principles including diffusion-limited growth and solid-liquid phase diagrams are treated in detail. In Sect. 2 technological aspects and various kind of growth systems including industrial versions are described. Section 3 summarizes the relevant properties of LPE grown layers. Section 4 contains the application of LPE to the material system InP/InGaAs/InGaAsP as a model system. In Sect. 5 the advantages and weaknesses of LPE with respect to device applications in comparison with competing methods are discussed, and finally we attempt to predict the future direction of LPE.